In this section, we will present the UWDG method for the KdV equation and the ZK equation on full grid, which serve as the building blocks of the adaptive multiresolution UWDG methods. Specifically, we review the UWDG method proposed in [1]} for the KdV equation.
Moreover, we develop a new UWDG method for the ZK equation with proofs on \(L^2\)  stability and optimal error estimates.
